Your impressions of the irascible Fiorello LaGuardia, mayor of the city between 1934 and 1945, just might depend on your theatergoing habits.

In a recent revival of the musical Fiorello! the Republican was portrayed as a tireless crusader against corruption in Tammany Hall. But in The Nance, the hilarious and heartbreaking new play by Douglas Carter Beane, he's a bully, intent on crushing the "corrupting moral influence" of the city's burlesque theaters.

LaGuardia is an offstage presence in The Nance, but he and his administration are a constant menace to the comics and chorines at the Irving Place Theater. The 1939 New York World's Fair is about to roll into town, and LaGuardia has authorized his licensing commissioner to close down burlesque houses and allowed the police force to bust up establishments where gay men were known to congregate.

One of La Guardia's most ardent admirers turns out to be Chauncey Miles, a burlesque performer famous for portraying a "nance," a comic character identified by his effete gestures, swooning voice, and double entendres. (Unlike most of his contemporaries, Chauncey happens to be gay in his personal life, which gives the theater owners anxieties of their own.) Despite all evidence to the contrary, Chauncey, a lifelong Republican, believes that the padlocks on theater doors and raids of gay meeting places are just stunts intended to win votes.

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Chauncey is aware that supporting an anti-gay administration makes about as much sense as—in his own words—a "Negro doing blackface." It's these and other contradictions that make Chauncey so riveting.

The role is tailor-made for the great Nathan Lane, and he brings to it his usual affable manner, insinuating inflections, and impeccable comic timing. But here there's also deep despair that seems to ooze from his pores.

Which doesn't mean that The Nance isn't amusing. The show is one of the most laugh-out-loud funny shows to hit Broadway in recent memory, both when it recreates the broad bits from the burlesque era and when its characters are engaging in offstage banter. "I forgot," Chauncey says when his limp-wristed mannerisms scandalize the other gay men at a restaurant, "there’s no camping allowed in this part of the forest."

Part of what makes The Nance so satisfying is that, at its center, it's a love story. When Chauncey picks up a handsome young man named Ned (a star-in-the-making turn by Jonny Orsini, who also shined last season in David Rabe's An Early History of Fire), doesn't hope for a minute that it will lead anywhere. In fact, Chauncey assumes it will end badly, perhaps with violence. "Is this the trade-smashing-in-the-queer's-face part?" he asks, only partly joking, when Ned bristles at being rebuffed.

Chauncey has a family of sorts in the other performers at the theater. This is where Beane, who delves deep with Chauncey and, to a lesser extent, with Ned, falters. Of the theater's trio of strippers, the only one who comes close to being more than a pencil sketch is a pants-wearing, card-carrying communist named Sylvie, played by the statuesque Cady Huffman. (It's a reunion of sorts, as Huffman played Ulla to Lane's Max Bialystock in The Producers.) She's a perfect foil for Chauncey, equally committed to her politics and disillusioned when her party kicks her to the curb.

The show's entire creative team is firing on all cylinders, starting with John Lee Beatty's marvelously detailed set, which earns its own round of applause as soon as the curtain comes up for its spot-on depiction of an art-deco automat. There's another ovation during curtain calls, when the set—which rotates between Chauncey's bathtub-in-the-kitchen flat, the garish stage, and the gritty backstage area—seems to take a victory lap of its own.

Japhy Weidman's lighting smartly highlights the architectural flourishes of the century-old Lyceum, transforming this gorgeous theater into a perfect stand-in for the Irving Place Theater. Leon Rothenburg's sound design subtly evokes everything from the muffled clatter of cutlery in a restaurant to the harsh whispers of an audience growing restless that, without warning, turn into angry jeers and epithets.

Ann Roth (who also designed Lane's fabulous frocks for the film The Birdcage) pulls out all the stops here, providing a long string of terrifically tacky outfits for the chorus girls. She does her best work with Chauncey himself, and I don't mean the fur-trimmed number he wears while playing a hooker named Hortense. His dapper suit, right down to the green carnation in the lapel, is exactly what a gay man of the period would wear when he wanted to be obvious, but only to others who knew the what to look for.

And did I mention the orchestra? Despite a near-constant stream of music, The Nance isn't technically a musical. So the presence of a five-piece orchestra, playing music by Glen Kelly, is icing on the cake. The songs, with lyrics by Beane himself, evoke the period without crossing over too far into pastiche. Expect to hear "Hi Simply Hi" at the piano bars someday soon.

There are a lot of balls to keep in the air, and director Jack O'Brien almost never misses. The pace flags a bit at the end of each of the play's two acts, but never so much that you feel antsy. In fact, when the curtain falls you might feel a little sad to see Chauncey go.

The Nance is playing at the Lyceum Theatre, 149 West 45th Street, between 6th and 7th avenues. Tickets range from $37 to $132 and are available at 212-239-6200 or www.telecharge.com.